The derivative of the function f is given by f'(x) = -3x + 4 for all x, and f(-1) = 6. Which of the following is an equation of the line tangent to the graph of f at x=-1

Question

The derivative of the function f is given by f'(x) = -3x + 4 for all x, and f(-1) = 6. Which of the following is an equation of the line tangent to the graph of f at x=-1

A) y= -3x +3

B) y= -3x +4

C) y= 7x +6

D) y= 7x+13

Answer 1

f(x) = (-3/2)x^2 + 4x + c

f(-1) = 6 = (-3/2)(-1)^2 + 4(-1) + c = -3/2-4 + c = -11/2 + c

c = 6+11/2 = 23/2

f(x) = (-3/2)x^2 + 4x + 23/2

f'(x) = -3x +4

f'(-1) = 3+4 = 7 = slope of the tangent line where x=-1

that means either C or D is correct. A and B have the wrong slope

D is correct. C has the wrong y intercept

the tangent line has slope = 7 and goes through the point (-1,6)

y=7x + b

6=-7 + b

b =13

tangent line is

y=7x + 13